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Simplifying x2 + 3x + -244 = 0 Reorder the terms: -244 + 3x + x2 = 0 Solving -244 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '244' to each side of the equation. -244 + 3x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + 3x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + 3x + x2 = 0 + 244 3x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 3x + x2 = 244 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 244 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 244 + 2.25 Combine like terms: 244 + 2.25 = 246.25 2.25 + 3x + x2 = 246.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 246.25 Calculate the square root of the right side: 15.692354826 Break this problem into two subproblems by setting (x + 1.5) equal to 15.692354826 and -15.692354826.Subproblem 1
x + 1.5 = 15.692354826 Simplifying x + 1.5 = 15.692354826 Reorder the terms: 1.5 + x = 15.692354826 Solving 1.5 + x = 15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 15.692354826 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.692354826 + -1.5 x = 15.692354826 + -1.5 Combine like terms: 15.692354826 + -1.5 = 14.192354826 x = 14.192354826 Simplifying x = 14.192354826Subproblem 2
x + 1.5 = -15.692354826 Simplifying x + 1.5 = -15.692354826 Reorder the terms: 1.5 + x = -15.692354826 Solving 1.5 + x = -15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -15.692354826 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.692354826 + -1.5 x = -15.692354826 + -1.5 Combine like terms: -15.692354826 + -1.5 = -17.192354826 x = -17.192354826 Simplifying x = -17.192354826Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.192354826, -17.192354826}
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